Active learning (AL), that aims to label limited data samples to effectively train the model, stands as a very cost-effective data labelling strategy in machine learning. Given the state-of-the-art performance GNNs have achieved in graph-based tasks, it is critical to design proper AL methods for graph neural networks (GNNs). However, existing GNN-based AL methods require considerable supervised information to guide the AL process, such as the GNN model to use, and initially labelled nodes and labels of newly selected nodes. Such dependency on supervised information limits both flexibility and scalabilty. In this paper, we propose an unsupervised, scalable and flexible AL method - it incurs low memory footprints and time cost, is flexible to the choice of underlying GNNs, and operates without requiring GNN-model-specific knowledge or labels of selected nodes. Specifically, we leverage the commonality of existing GNNs to reformulate the unsupervised AL problem as the Aggregation Involvement Maximization (AIM) problem. The objective of AIM is to maximize the involvement or participation of all nodes during the feature aggregation process of GNNs for nodes to be labelled. In this way, the aggregated features of labelled nodes can be diversified to a large extent, thereby benefiting the training of feature transformation matrices which are major trainable components in GNNs. We prove that the AIM problem is NP-hard and propose an efficient solution with theoretical guarantees. Extensive experiments on public datasets demonstrate the effectiveness, scalability and flexibility of our method. Our study is highly relevant to the track "Graph Algorithms and Modeling for the Web" since we focus one of the major listed topics "Graph Embedding and GNNs for the Web" and AL for GNNs, as an important research problem, is faced by aforementioned challenges to be tackled in this paper.

In this work, we address the critical task of discovering representative time series in exploratory data mining. We define a representative time series, referred to as similarity-bounded representative time series, as one that represents other time series if their similarity meets a user-defined threshold. Building on this definition, we study the problem of finding the smallest set of such time series that can represent a specified proportion of all time series within the dataset. The representativeness of each similarity-bounded representative time series is controllable and determined by the specified level of similarity, and only the minimum number of such representatives needed to collectively represent the specified proportion of entire set are identified. Identifying representative time series over large-scale data in an efficient and effective manner facilitates exploratory data analysis and summary generation, serving a wide range of data exploration applications across diverse domains. We first prove the NP-hardness of this problem and propose a range of approximation methods with theoretical guarantees, and we refer to them as non-learning-based methods. While effective, these methods often excel in either running time or memory efficiency, but not both concurrently. To overcome these limitations, we further propose a learning-based method that simultaneously optimizes both time and memory efficiency. This method leverages novel data preparation and training strategies, providing adaptability to user-specified representativeness requirements with low memory usage and computational overhead. We conduct extensive experiments across four real-world datasets to demonstrate that our learning-based method is highly competitive with non-learning-based methods in terms of effectiveness (produces similar number of representative time series), while achieving significantly higher efficiency (up to 21× speedups) and lower memory consumption (saving up to 101× memory space).